College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 4, Exponential and Logarithmic Functions - Chapter 4 Review - Concept Check - Page 425: 58


$x = 7$

Work Step by Step

To solve the given exponential equation, make the two sides have the same base. Then, equate the exponents and solve for the unknown variable. Since $125=5^3$, the given equation is equivalent to: $5^{4-x} = \dfrac{1}{5^3}$ Use the rule $\dfrac{1}{a^m} = a^{-m}$ to obtain: $5^{4-x} = 5^{-3}$ Use the rule $a^m = a^n \longrightarrow m=n$ to obtain: $4-x=-3$ Subtract $4$ to both sides to obtain: $-x = -7$ Multiply $-1$ to both sides to obtain: $x = 7$
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